In the restoration of noisy-blurred images, we have trade-off problem between smoothing the noise and restoring the edge regions. While the noise is smoothed, the edges or details will become corrupt. On the other hand, restoring the edges will amplify the noise making it more prominent. To solve this problem we should choose regularization operators suited separately for flat regions and edges. In this paper, we propose an adaptive algorithm, which uses an I-H regularization operator for flat regions and a Laplacian regularization operator for edge regions. Consequently, good restoration quality was observed in both regions. There was less noise amplification and ringing artifacts with better ISNR than in conventional restoration.